This paper is dealt with the Theory of fixed points of mappings which are an analogue like contraction mapping and Kannan mappings over a locally convex topological vector space. Some common fixed point Theorems for a pair of mappings involving their iterates have been proved. The purpose of this paper is to examine the validity of established results on fixed points of contraction mappings and Kannan mappings over such a locally convex topological vector space. It is revealed that a suitable local base in locally convex topological vector space plays an important role to find fixed points of above mappings over it. Also an application relating to stability of fixed point equation for Kannan-type contractive mappings is obtained here.